İstanbul Üniversitesi İşletme Fakültesi Dergisi Istanbul University Journal of the School of Business Administration Cilt/Vol:38, Sayı/No:1, 2009, 47-65 ISSN: 1303-1732 - www.ifdergisi.org © 2009 Prediction of business failure: a comparison of discriminant and logistic regression analyses Bengü Vuran1 Finance Department, Faculty of Business Administration Istanbul University, Istanbul, Turkey Abstract This paper investigates two predictive models of business failure and important financial variables detecting failure potential using the sample of 122 both publicly opened and closed firms from the period of 1999-2007. Discriminant and Logistic Regression Analyses are performed and their predictive accuracy are compared. The results demonstrate that most of the failed firms show the signs of financial distress long before the failure and no statistically significant difference between the prediction results and variable choice of the discriminant and logistic regression analyses. Keywords: Business Failure, Failure Prediction, Discriminant Analysis, Logistic Regression Analysis, Financial Distress. Finansal başarısızlığın tahmini: diskriminant ve lojistik regresyon analizlerinin karşılaştırılması Özet Bu çalışma; 1997-2007 döneminde halka açık ve halka kapalı toplam 122 işletmeden oluşan örneklem ile iki istatistiksel yöntem kullanarak işletmelerin finansal başarısızlığı bir ve iki yıl öncesinden tahmin etmeye ve finansal başarısızlığın öngörülmesinde yararlı olan finansal oranları ortaya çıkarmaya çalışmaktadır. Çalışmada Diskriminant ve Lojistik Regresyon Analizleri uygulanmış ve modellerin tahmin güçleri karşılaştırılmıştır. Sonuçlar; finansal başarısızlığa uğramış işletmelerin çoğunun finansal sıkıntı belirtilerini başarısızlıktan çok önce gösterdiklerine ve çalışmada kullanılan yöntemlerin arasında tahmin gücü ve değişken seçimi konusunda istatistiki açıdan önemli fark olmadığına işaret etmektedir. Anahtar Kelimeler: İşletmelerde Finansal Başarısızlık, Başarısızlık Tahmini, Diskriminant Analizi, Lojistik Regresyon Analizi, Finansal Sıkıntı. 1. Introduction Business failure is the situation that a firm can not pay lenders, suppliers, shareholders, etc., or a bill is overdrawn or the firm is bankrupt according to the law. All of these situations result in a discontinuity of the firm’s operations. Business failure is a worldwide problem. The number of failing firms is important for the economy of a country and it can be considered as an index of the development and the robustness of the economy. The ability to predict firm failure has drawn considerable attention from numerous researchers and practitioners. The importance of such efforts is obvious. Business failure is an indication of resource misallocaion which is undesirable from a social point of view. An early warning signal of probable failure will enable both management and investors to take preventive measures; operating policy change, reorganization of financial structure 1 [email protected] (B. Vuran) 47 B. Vuran / İstanbul Üniversitesi İşletme Fakültesi Dergisi 38, 1, (2009) 47-65 © 2009 and even voluntary liquidation will usally shorten the lenght of time losses incurred and thereby improve both private and social resource allocation. The development and use of models can be very important in two different ways. First, as “early warning systems” such models are very useful to managers, authorities… etc. That can act to prevent failure. These actions include the decision about merger of the distress firm, liquidation or reorganization type.[1] Second, such models can be usuful in aiding decision making of financial institutions in firms’ evluation and selection. Decisions about credit-granting, investment etc., have to take into account the opportunity cost as well as the risk of failure. The following secton briefly reviews some of the previous studies of business failure. Data and description of research design are explained in the third section. The fourth section presents the emprical results. Conclusions of the findings are given in the last section. 2. Literature Review A large number of methodologies and models have been presented in business failure literature. The first studies, univariate ones, were about the usefullness of financial ratios and most of the analyses are viewed as descriptive statistics. Fitzpatrick [2] found that Net Income to Net Worth and Net Worth to Debt were the variables which are capable of predicting the risk of failure. Winakor and Smith [3] proposed Working Capital / Total Assets ratio as the best indicator of approaching failure. Merwin [4] observed three important ratios six years before failure: Working Capital / Total Assets, Net Worth / Total Debts and Current Assets / Current Liabilities. Beaver [5] introduced a univariate techniques for the classification of firms in two groups, using some financial ratios.The ratios providing the highest discrimination capability were Cash Flow / Total Debts, Net Income/ Total Assets and Total Debts/ Total Assets. Altman [6] was the first to use multivariate analysis to analyze the ratios of various bankrupt and nonbankrupt groups and to examine the effect of using different combinations of financial ratios to predict business failure. Also in 1993, Altman devised a four-variable model that established different weights for the various ratios and new cut-off values to categorize firms as bankrupt and nonbankrupt. Deakin [7] modified the Altman model to include thr 14 best ratios identified by Beaver (1966) in his univariate study. He used the version of Multiple Discriminant Analysis (MDA) which assigns the probability of membership to the failed and nonfailed groups on the basis of its Z scores in previous years. Edmister [8] developed and tested a number of methods of analyzing financial ratios to predict the failure of small businesses. He concluded that the predictive power of ratio analysis depends upon both the choice of analytical method and the selection of ratios. Unlike Altman and Beaver who found that one financial statement is sufficient for accurate classification, Edmister concluded that three consecutive statements are required for effective analysis of small businesses. Blum [9] constructed an MDA to assess the probability of failure using twelve financial ratio and twelve nonfinancial indicators. The data were divided into twenty one ranges of at least three years and a discriminant function was fitted to half of the data in each range. Moyer [10] pointed out that Altman’s (1968) model had poor predicting ability and he had used a stepwise discriminant analysis to construct a model providing higher classification ability. 48 B. Vuran / İstanbul Üniversitesi İşletme Fakültesi Dergisi 38, 1, (2009) 47-65 © 2009 Altman, Haldeman and Narayanan [11] developed the revised version of Altman’s original discriminant function which they refer to as “ZETA Model”.This was done to base the estimation on larger companies, update the sample period and adopt the new accounting practices. Casey and Bartczak [12] added cash flow variables to six acrual based variables in a discriminant model to see whether their inclusion improved the explanatory power of the model. Other researchers to focus on cash flow variables in MDA were Castanga and Matolcsy [13], Gombola, Haskins, Ketz and Williams [14], Aziz, Emmanuel and Lawson [15] and Aziz and Lawson [16]. Some of the other studies employing discriminant analysis for business failure prediction were Collongues [17], Conan Holder [18], Dmbolena and Khoury [19], Izan [20], Micha [21], Friedman et al. [22], Falbo [23], Laitinen [24] and Louma and Laitinen [25]. Multivariate conditional probability models (logit and probit analyses) were later introduced into failure prediction literature. Logit analysis for the prediction of business failure was firstly proposed by Ohlson [26]. Other researchers extended the basic techiques of logit analysis to obtain better classification accuracy. Zavgren [27] developed a measure of information contained in a logistic function to assess the uncertainty of unexpected failure. Peel and Peel’s[28] study involved British listed companies, the data was gathered for three years prior to bankruptcy and various multilogit models were generated. This enabled researchers to generate probabilities for a company failing one year ahead, two and three years ahead or remaining healty. Keasey, McGuiness and Short [29] developed a similar multilogit model to classify firms according to the time they are expected to fail. Lau [30] defined five states in her study: non-failure, passing the dividend, default on a loan, debt reorganization and bankruptcy. Models were developed using ten explanatory variables from one, two and three year horizon. Generaly the models performed quite well, especially classifying the financially healty firms as non-failures. Subsequent studies adopted an identical approach, Bahson and Bartley [31], Ward [32], Ward and Foster [33] have reported similar results. Gentry, Newbold and Whitford’s [34] study complemented Casey and Bartzcak’s [12] study which investigates the cash-based funds flow ratios can adequately classify failed and nonfailed firms. Their logit findings substantiated Casey and Bartzcak findings that cash flow from operations doesn’t improve the classification results where as dividends fund flows was significant in distinguishing between failed and nonfailed companies. Because of limitations of discriminant analysis, logit analysis was prefered by researchers. However, comparative studies between two methods (Press and Wilson [35], Collins and Green [36]) have not proved a higher classification accuracy for all cases and types of samples. Hamer [37] compared discriminant analysis to logit method for different data sets concluding that the models derived are of comparable ability to assess the probability of failure. 3. Data and Methodology The purpose of this research is to construct bankruptcy prediction models, identify which financial ratios are of particular interest in predicting bankruptcy and to compare the prediction power of models. The sample consists of 169 manufacturing firms totally, 78 financially unsuccessful and 91 successful during the period 1997- 2007. Experiencing financial distress, defaulting on loan obligations, making an explicit agreement with creditors to reorganize debt structure and going bankruptcy are accepted as financial failure criteria of the study. Failing firms are randomly macthed with healty firms and on 49 B. Vuran / İstanbul Üniversitesi İşletme Fakültesi Dergisi 38, 1, (2009) 47-65 © 2009 the basis of industry classification and the financial statement date. Ratios selected for this study have been promoted by theorists or have been found to be significant predictors of business failure in previous emprical researches. The year of failure for unsuccessful firms is selected as the year in which the firm undergoes financial distress. For publicly-opened firms, this information is gathered inspecting the “company news” section in the web site of Istanbul Stock Exchange (ISE), for publicly-closed firms, it is available in Dun& Bradstreet database. Previous studies have largely ignored publicly-closed firms because of the difficulty of obtaining data. But this research is the first one in Turkey incorporating publicly-closed firms into business failure analysis. The data of publicly-closed firms are gathered from Dun&Bradstreet regional office while that of publicly-opened firms are from Istanbul Stock Exchange. Of the 169 firms, 95 are publicly-closed and 74 are publicly-opened. Because only two consecutive annual financial statements of publicly-closed firms are available prior to failure date, the prediction horizion is choosen as two years prior to failure and the “cash flow from the operation” components can be computed for only first year before failure. Discriminant analysis is choosen as the first analysis in this research because of its pioneering characteristic in literature. Discriminant analysis imposes certain statistical requirements on predictors: multivariate normality of independent variables and equal variance-covariance matrices of groups. Because of these prerequisites, the distribution of financial ratios of 169 firms are examined and it is seen that the normality requirement is violated. The data is examined for the presence of outliers, thus the outlier analysis is performed. After extraction of outliers, it is observed that multinormality is provided and the sample size reduced to 122 firms, 51 unsuccessful and 71 successfull. Of these are 82 publicly-closed and 40 puclicly-opened firms. In order to compare the predicting power of the models, it is continued to work with 122 firms although logistic regression analysis doesn’t have strict assumptions like discriminant analysis. Because of the large number of variables found to be significant indicators of corporate problems in past studies, a list of 30 potentally helpfull ratios is complied for evaluation. These ratios are classified into eight standart ratio categories. Table I presents 30 financial ratios used in the model. 50 B. Vuran / İstanbul Üniversitesi İşletme Fakültesi Dergisi 38, 1, (2009) 47-65 © 2009 Table 1: Independent Variables Of Models FINANCIAL RATIOS Current Assets / Current Liabilities CATEGORY Liquidity (Current Assets – Inventories ) / Current Liabilities Liquidity (Cash + Bank) / Current Liabilities Liquidity Sales / Accounts Receivable Cost of Goods Sold / Inventories Activity Activity Sales / Current Assets Activity Sales / Fixed Assets Activity Sales / Tangible Fixed Assets Activity Sales / Total Assets Activity Sales / Total Equity Activity Gross Profit / Sales Profitability Earnings Before Interest and Taxes / Sales Net Profit / Sales Profitability Profitability Net Profit / Total Equity Profitability Net Profit / Total Assets Profitability Total Debt / Total Assets Financial Structure Short Term Debt / Total Assets Long Term Debt / Total Assets Financial Structure Financial Structure Total Debt / Total Equity Financial Structure Total Equity / Total Assets Asset Financing Fixed Assets / Total Equity Fixed Assets / ( Total Equity + Long Term Debt ) Asset Financing Asset Financing Tangible Fixed Assets / Total Equity Asset Financing Current Assets / Total Assets Fixed Assets / Total Assets Asset Structure Asset Structure Tangible Fixed Assets / Total Assets Asset Structure Cash Flow From Operations / Interest Expense Cash Flow Net Sales Total Equity Size Size Total Assets Size Multicollinearity, usually found in financial data, was as high as might be expected. So, to eliminate multicollinearity, a different method of data reduction is applied in this study. The amount of variables to be included in the model is selected by correspondence analysis. First, the Kendall’s coefficient of concordance is calculated for each ratio group. This coefficient is used to measure the degree of correspondence between two rankings and the assessing the significance of this correspondence [38]. In other words, it measures the strenght of associations between variables of a ratio group. If correspondence is significant, then, Spearman’s rank correlation coefficient is calculated in order to choose representative ratio of each category. From the original list of variables, for each category except for the asset structure, because the Kendall’s coefficient of concordence can’t not be found significant for this 51 B. Vuran / İstanbul Üniversitesi İşletme Fakültesi Dergisi 38, 1, (2009) 47-65 © 2009 group, so all ratios of this group are added into the analysis, a ratio is selected as the representative for each category. Totally; 10 and 9 variables are selected as a result of correspondence analysis one and two year prior to failure respectively.Table 2 and Table 3 exhibits the representative ratios for each group. Table 2: Representative Ratios for Each Ratio Category One Year Prior to Failure CATEGORY REPRESENTATIVE RATIO Liquidity Activity Profitability Financial Structure Asset Financing Size Cash Flow Asset Structure Current Assets / Current Liabilities Sales / Total Assets Net Profit / Total Assets Total Debt / Total Assets Fixed Assets / Total Equity Total Assets Cash Flow From Operations / Interest Expense Current Assets / Total Assets Fixed Assets / Total Assets Tangible Fixed Assets / Total Assets Table 3: Representative Ratios for Each Ratio Category Two Year Prior to Failure CATEGORY Liquidity Activity Profitability Financial Structure Asset Financing Size Asset Structure REPRESENTATIVE RATIO (Current Assets – Inventories ) / Current Liabilities Sales / Total Assets Net Profit / Total Assets Short Term Debt / Total Assets Fixed Assets / Total Equity Total Assets Current Assets / Total Assets Fixed Assets / Total Assets Tangible Fixed Assets / Total Assets Discriminant and Logistic Regression analyses are conducted with the representative ratios one and two year prior to failure using SPSS program. To select the best set of discrminating ratios stepwise selection criteria is applied. The emprical results are explained in the next section. 4. Emprical Results An important issue before conducting the models is to determine the individual discriminating ability of the variables, so F Test is performed. This test relates the difference between the average values of the ratios in each group to the variability of values within each group. In Table 1 and Table 2, the resulting F statistics are presented for one and two year prior the failure respectively. 52 B. Vuran / İstanbul Üniversitesi İşletme Fakültesi Dergisi 38, 1, (2009) 47-65 © 2009 Table 4: Test of Equality of Group Means One Year Prior to Failure Te sts of Equality of Group Means ca_c l td_ta f a_teq sales_f a np_ta tassets cf o_int tfa_ta ca_ta f a_ta Wilks' Lambda ,872 ,659 ,971 ,996 ,669 ,988 ,854 ,962 ,988 ,988 F 17,663 62,138 3,564 ,524 59,490 1,442 20,505 4,735 1,437 1,437 df 1 1 1 1 1 1 1 1 1 1 1 df 2 120 120 120 120 120 120 120 120 120 120 Sig. ,000 ,000 ,061 ,471 ,000 ,232 ,000 ,032 ,233 ,233 Table 5: Test of Equality of Group Means Two Year Prior to Failure Te sts of Equality of Group Means acidtest np_ta ta sales_f a std_ta f a_teq tfa_ta ca_ta f a_ta Wilks' Lambda ,874 ,810 ,982 ,995 ,754 ,974 ,931 ,969 ,969 F 17,244 28,118 2,196 ,579 39,246 3,255 8,854 3,894 3,894 df 1 1 1 1 1 1 1 1 1 1 df 2 120 120 120 120 120 120 120 120 120 Sig. ,000 ,000 ,141 ,448 ,000 ,074 ,004 ,051 ,051 As it is seen in Table 1, one year prior to failure, Current Asset / Current Liabilities (ca _cl), Total Debt / Total Assets (td _ta) , Net Profit / Total Assets (np_ta) and Cash Flow From Operation / Interest Expense (cfo _int) ratios and In Table 2, two year prior to failure, (Current Assets – Inventories)/ Current Liabilities (Acidtest), Net Profit / Total Assets (np_ta), Short Term Debt / Total Assets (std_ta) ratios are all significant at 0,000 indicating extremely significant differences between failed and healty groups. The aforementioned ratios are expected to be the large contributors to group seperation in conducted models. 4.1. Results for One Year Prior to Failure 4.1.1. Discriminant Model One Year Prior to Failure Discriminant analysis identifies a set of variables that “best” discriminates between the two groups.The sensitivity of discriminant analysis is based on the validity of the assumptions [39].Besides the multivariate normality, the second distinctive assumption of discriminant analysis is the equality of variance covariance matrices across groups. 53 B. Vuran / İstanbul Üniversitesi İşletme Fakültesi Dergisi 38, 1, (2009) 47-65 © 2009 The hypothesis tesing of equality of covariance matrices is checked by Box’s M test. As it is shown in Table 6, the null hypothesis of equal population covariance is accepted (Sig. 23,7 % ). Table 6: Box’s M Test Results of Discriminant Model One Year Prior to Failure Te st Res ults Box's M F 8,241 Approx. 1,335 df1 6 df2 79519,470 Sig. ,237 Tests null hypothesis of equal population covariance matrices . Table 7: The Canonical Discriminant Coefficients of Discriminant Model 0ne Year Prior to Failure Canonical Discrim inant Function Coe fficie nts td_ta np_ta cf o_int (Cons tant) Func tion 1 -2,856 4,796 ,188 ,683 Unstandardized coeff icients Using the canonical discriminant function coefficients, the discriminant model one year prior to failure can be written as, Z = 0,683 + 0,188 Cash Flow From Operations / Interest Expense + 4,796 Sales / Total Assets – 2,856 Total Debt / Total Assets In the discriminant function, each weight represents the relative contribution of its associated variable to the function. The sign denotes that the variable makes either a positive or a negative cotribution it doesn’t indicate the direction of the relationship [40]. The classification results are given in Table 8 indicating that the discriminant model classifies 84,4 % of the firms correctly. Table 8: The Classification Results Of Discriminant Model One Year Prior to Failure Clas sification Re sultsa Original Count % state ,00 1,00 ,00 1,00 Predicted Group Members hip ,00 1,00 42 9 10 61 82,4 17,6 14,1 85,9 Total a. 84,4% of original grouped cases correctly classif ied. 54 51 71 100,0 100,0 B. Vuran / İstanbul Üniversitesi İşletme Fakültesi Dergisi 38, 1, (2009) 47-65 © 2009 Another objective of discriminant analysis is to classify future observations into one of the two groups. The proportional chance criterion is calculated in order to test the classification capability of discriminant function for future observations. If the percentage of correct classifications is higher than would be expected by chance it can be concluded that the discriminant model provides meaningfull information in classification. Proportional chance criterion is calculated as; [41] CPRO = p2 + ( 1-p )2 where; p = proportion of firms in group 1 1-p = proportion of firms in group 2 Using the groups proportions (71/122 healty and 51/122 failing) proportional chance criterion is calculated as 51,28 %. Therefore, the actual prediction rate of 84,4 % may be acceptable because it is above the proportional chance criterion. This means that when new companies are classified, the nature of the model is predictive. 4.1.2. Logistic Regression Model One Year Prior to Failure Logistic regression is an attractive alternative to discriminant analysis.Its emprical results parallel those of multiple regression in terms of their interpretation and the casewise diagnostic measures available for examining residuals and it handles categorical independent variable easily whereas in discriminant analysis the use of dummy variables created problems with the variance covariance equalities. Logistic regression requires less restrictive statistical assumptions so the use of logit analysis esentially avoids all of the problems discussed with respect to discriminant analysis. Even if the assumptions are met, many researchers prefer logistic regression because it is similar to multiple regression. It has straightforward statistical tests, similar approaches to incorporating metric and nonmetric variables and nonlinear effects [42]. Before the estimation process begins, Hosmer and Lemeshow test is used to measure the overall fit of the model. This statistical test measures the correspondence of the actual and the predicted values of the dependent variable. The null and alternative hypotheses for assessing the overall model fit are; H0 : The hypothesized model fits the data. HA : The hypothesized model does not fit the data. Table 9: Hosmer Lemeshow Test for Overall fit of Logistic Regression Model for One Year Prior to Failure Hosm er and Lem e show Te st Step 1 2 3 Chi-square 7,249 6,959 10,326 df 8 8 8 Sig. ,510 ,541 ,243 As it is seen in Table 9, In Step 3, the null hypothesis is accepted (Sig. 24,3 % ). After the overall fit of the model has been assessed, using Table 10, the logistic regression model can be written as, L = 1,403 + 0,351 Cash Flow From Operations / Interest Expense + 9,541 Sales / Total Assets – 4,418 Total Debt / Total Assets 55 B. Vuran / İstanbul Üniversitesi İşletme Fakültesi Dergisi 38, 1, (2009) 47-65 © 2009 Table 10: Variables of Logistic Regression Model One Year Prior to Failure Variable s in the Equation Step a 1 Step b 2 Step c 3 td_ta Constant td_ta np_ta Constant td_ta np_ta cf o_int Constant B -6,268 3,839 -4,144 11,192 S.E. 1,139 ,688 1,262 3,242 Wald 30,266 31,128 10,787 11,918 2,186 ,807 -4,418 9,541 ,351 1,403 1,326 3,311 ,164 ,881 df 1 1 1 1 Sig. ,000 ,000 ,001 ,001 Exp(B) ,002 46,477 ,016 72525,949 7,331 1 ,007 8,900 11,099 8,304 4,587 2,539 1 1 1 1 ,001 ,004 ,032 ,111 ,012 13925,546 1,420 4,068 a. Variable(s ) entered on s tep 1: td_ta. b. Variable(s ) entered on s tep 2: np_ta. c. Variable(s ) entered on s tep 3: cf o_int. The Wald statistic is used to assess statistical significance of coefficents. While Total Debt / Total Asset and Net Profit / Total Asset ratios are significant at an alpha level of 0,01, Cash Flow From Operations / Interest Expense ratio is significant at an alpha level of 0,05. The sign of the original coefficients indicates the direction of relationship. A positive coefficient increases the probabiliy whereas the negative value decreases the prediced probability, because the original coefficients are expressed in terms of logit values. Table 11: The Classification Results of Logistic Regression Model One Year Prior to Failure Clas sification Tablea Predicted state Step 1 Observed state Step 2 Overall Percentage state Step 3 Overall Percentage state Overall Percentage ,00 1,00 ,00 1,00 34 12 17 59 ,00 1,00 40 8 11 63 ,00 1,00 42 10 9 61 Percentage Correct 66,7 83,1 76,2 78,4 88,7 84,4 82,4 85,9 84,4 a. The cut v alue is ,500 The classification results show that before one year before the failure, logistic regression model predicted 84,4 % of the firms accurately. 56 B. Vuran / İstanbul Üniversitesi İşletme Fakültesi Dergisi 38, 1, (2009) 47-65 © 2009 It is seen that, both models selected the same ratios; the Cash Flow From Operations / Interest Expense which is the cash-based version of times interest earned ratio ( Ebit / Interest ) , Net Profit /Total Assets and Total Debt / Total Assets, as the best discriminator ratios between the failing and the healty firms one year prior to failure. 4.2. Results for Two Years Prior to failure 4.2.1. Discriminant Model Two Year Prior to Failure The hypothesis tesing of equality of covariance matrices is done by Box’s M test. As it is shown in Table 12, the null hypothesis of equal population covariance is accepted.(Sig. 42,6%) Table 12: Box’s M Test Results of Discriminant Model Two Year Prior to Failure Te st Res ults Box's M F Approx. df1 df2 Sig. 2,837 ,928 3 978423,0 ,426 Tests null hypothesis of equal population covariance matrices . Table 13: The Canonical Discriminant Coefficients of Discriminant Model for Two Year Prior to Failure Canonical Discrim inant Function Coe fficie nts np_ta std_ta (Cons tant) Func tion 1 -7,202 3,399 -1,108 Unstandardized coeff icients The discriminant model can be written as; Z = - 1,108 + 3,3999 Short Term Debt / Total Assets – 7,202 Sales / Total Assets In Table 14, the classification results indicate that discriminant model classifies 84,5 % of the healty firms and % 74,5 of the failing firms correctly. The overall clssification accuracy of the model is 80,3 % . Table 14: The Classification Results Of Discriminant Model Two Year Prior to Failure Clas sification Re sultsa Original Count % state ,00 1,00 ,00 1,00 Predicted Group Members hip ,00 1,00 38 13 11 60 74,5 25,5 15,5 84,5 Total 51 71 100,0 100,0 a. 80,3% of original grouped cases correctly classified. 57 B. Vuran / İstanbul Üniversitesi İşletme Fakültesi Dergisi 38, 1, (2009) 47-65 © 2009 The correct classification ratio (80,3 %) exceeds the proportional chance criterion (51,28 %) which proves that model’s prediction ability is significantly better than chance. 4.2.2. Logistic Regression Model Two Year Prior to Failure As seen in Table 15, the Hosmer Lemeshow test results show the significance level of 0,146 indicating that the model fit is acceptable. Table 15: Hosmer Lemeshow Test for Overall fit of Logistic Regression Model Two Year Prior to Failure Hosm er and Lem e show Te st Step 1 2 Chi-square 6,399 12,115 df 8 8 Sig. ,603 ,146 The logistic regression model can be written using Table 15 as, L = 1,606 – 3,908 Short Term Debt / Total Assets + 10, 946 Sales / Total Assets Table 16: Variables of Logistic Regression Model Two Year Prior to Failure Variable s in the Equation Step a 1 Step b 2 std_ta Constant np_ta std_ta Constant B -4,941 2,764 10,946 -3,908 S.E. ,993 ,542 3,607 1,037 Wald 24,765 26,012 9,207 14,207 1,606 ,622 6,658 df 1 1 1 1 Sig. ,000 ,000 ,002 ,000 Exp(B) ,007 15,860 56734,965 ,020 1 ,010 4,983 a. Variable(s ) entered on s tep 1: std_ta. b. Variable(s ) entered on s tep 2: np_ta. The Logistic Regression model for two year prior to failure includes two variables; Short Term Debt / Total Assets and Net Profit / Total Assets, with logistic coefficients of -3,908 and 10,946 respectively and a constant of 1,606 (Table 16). Comparing these results to dicriminant model reveals almost identical results, as discriminant model included same variables / ratios. The classification results demonstrate that the model has predictive accuracy of 78,4 % for failing, 84,5 % for healty and 82 % for overall. (These results are presented in Table 17) The logit model correctly classified 78,4 % of failing, 84,5 % of healty and 82 % of total firms. 58 B. Vuran / İstanbul Üniversitesi İşletme Fakültesi Dergisi 38, 1, (2009) 47-65 © 2009 Table 17: The Classification Results of Logistic Regression Model TwoYear Prior to Failure Clas sification Tablea Predicted state Step 1 Observed state Step 2 Overall Percentage state ,00 1,00 ,00 1,00 30 12 21 59 ,00 1,00 40 11 11 60 Overall Percentage Percentage Correct 58,8 83,1 73,0 78,4 84,5 82,0 a. The cut v alue is ,500 The accuracy of the models is also evaluated on the basis of Type I (predicting a failed firm not to fail) and Type II (predicting a healty firm to fail ) errors. One year prior to failure, both discriminant and logistic models produce identical rates of Type I and Type II error, 7,3 % and 8,2 % respectively. Two years prior te failure, the Type I error of discriminant model proves to be 11 % while the Type II error is even better at 9 %. The logit model has identical rate, 9 %, of Type I and Type II error. 5. Summary and Conclusion This study develops and empirically tests two business failure prediction models. Both linear multiple discriminant and logistic regression analyses are conducted one and two years prior to failure. Stepwise procedure is applied in order to avoid multicollinearity while systematically selecting variables. Besides publicly opend firms, the study also incorporates the publicly closed firms into the sample which is not done until today in our country because of many important problems pertaining to the development of their data. The time period studied here spanned two years. One year prior to failure, the results indicate that three ratios which are statistically significant for the purpose of assessing the probability of failure. These are (i) total asset profitability, (ii) the financial structure as reflected by a measure of leverage (iii)some measure of current liquidity (Cash Flow from Operations / Interest Expense ). Two year prior to failure, the models identified two significant variables that help discriminating between two groups of firms (i) a measure of profitability (ii) a measure of leverage. In both years and in both models, the “Net Profit / Total Asset” variable which has the highest coefficient, provided the most significant information in classifying failed and healty firms. The leverage ratio ranks in second in its contribution to the overall prediction and classification ability of the models. CFO, operating cash flow measure contributed information to improve the classification accuracy of the models for the first year before failure and this component improved the classification rate of failed and healty companies. The Cash Flow From Operations component can not be computed for the second year before failure lacking of financial statements of puclicy–closed firms for three years 59 B. Vuran / İstanbul Üniversitesi İşletme Fakültesi Dergisi 38, 1, (2009) 47-65 © 2009 before the failure. So the impact of cash flow ratio in discrimination of the firms two years prior to failure can not be assessed. The profitability ratio offers a reasonable measure of management effectiveness; the leverage ratios represent historical reasons to business failure, reasons that are directly related to the excessive or unwise use of leverage and the cash flow ratio constitutes a necessary measure of solvency. Predictive accuracy of discriminant model amounts to 84,4 % at the first year and 80,1 % at the second year before the failure. The misclassification rate of failed firms (Type I error) is smaller than the misclassification rate of healty firms (Type II error) one year prior to failure but the reverse is true for the second year before failure. Logistic regression model achieves 84,4 % at the first year and 82 % at the second year before the failure. The misclassification rate of failed firms (Type I error) is less than the misclassification rate of healty firms (Type II error) in the first year like discriminant model, and equal rates of both types of errors are observed in the second year before the failure. The classification results show that no statistically significant difference between the results for each of the two years before bankruptcy, regardless of whether the logit or the discriminant model is used. As a summary; The profitability ratio prevailed as the most significant indicators in both years, The degree of leverage was found to be important in both years, Although acid test ratio is expected to be a significant indicator two years prior to failure, existence of high correlation (59,6 %) between this ratio and leverage ratio lead the stepwise procedure choose the other one. 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